In this subsection, we study the convergence rate of our proposed \(T^{f_d}_R\) , i.e., the rate at which its approximation error goes to zero, when the domain interval diameter \(d(\mathbb {I}\mathcal {Z})\) 
shrinks. We show that when using \(T^{f_d}_R\) , the error converges at least linearly, which is also the convergence rate of natural inclusions \(T^{f}_N\)  [1]}. Further, we show that the subdivision principle introduced in [2]} can be applied to improve the convergence. We first introduce the notion of convergence rate, inspired by [2]}, and then, we present the convergence rate and the subdivision principle for our proposed \(T^{f_d}_R\) .
